Effect of perfluorosulfonic acid side chains on oxygen permeation in hydrated ionomers of PEMFCs: Molecular dynamics simulation approach


 We prepared two types of perfluorosulfonic acid (PFSA) ionomers with Aquivion (short side chain) and Nafion (long side chain) on a Pt surface and varied their water contents (2.92 ≤ λ ≤ 13.83) to calculate the solubility and permeability of O2 in hydrated PFSA ionomers on a Pt surface using full atomistic molecular dynamics (MD) simulations. The solubility and permeability of O2 molecules in hydrated Nafion ionomers were greater than those of O2 molecules in hydrated Aquivion ionomers at the same water content, indicating that the permeation of O2 molecules in the ionomers is affected not only by the diffusion coefficient of O2 but also by the solubility of O2. Notably, O2 molecules are more densely distributed in regions where water and hydronium ions have a lower density in hydrated Pt/PFSA ionomers. Radial distribution function (RDF) analysis was performed to investigate where O2 molecules preferentially dissolve in PFSA ionomers on a Pt surface. The results showed that O2 molecules preferentially dissolved between hydrophilic and hydrophobic regions in a hydrated ionomer. The RDF analysis was performed to provide details of the O2 location in hydrated PFSA ionomers on a Pt surface to evaluate the influence of O2 solubility in ionomers with side chains of different lengths. The coordination number of C(center)–O(O2) and O(side chain)–O(O2) pairs in hydrated Nafion ionomers was higher than that of the same pairs in hydrated Aquivion ionomers with the same water content. Our investigation provides detailed information about the properties of O2 molecules in different PFSA ionomers on a Pt surface and with various water contents, potentially enabling the design of better-performing PFSA ionomers for use in polymer electrolyte membrane fuel cells.


Introduction
Polymer electrolyte membrane fuel cells (PEMFCs) are environmentally friendly energy sources that can alleviate environmental problems because of their low emissions of environmental pollutant gases such as SOx, NOx, CO2, and CO. 1,2 PEMFCs have been used in various applications such as fuel-cell vehicles and power supplies (including portable power supplies) because, in addition to their ecofriendly benefits, PEMFCs can also generate high power densities and operate with short start-up times because of their low operating temperature. 1,[3][4][5] In general, PEMFCs consist of membrane electrode assembly (MEA) layers, gas-diffusion layers, microporous layers, gas flow channels, and bipolar plates. 3 The MEA layers are especially important because the cell performance and durability of PEMFCs are strongly affected by the design and composition of their MEA layers. 4 MEA layers in a PEMFC system comprise catalyst layers (CLs) and a polymer membrane; the polymer membrane plays a critical role in transferring protons from the anode to the cathode in the process of generating electricity. 5 CLs also play a critical role because the electrochemical reactions related to energy conversion in a PEMFC, such as the hydrogen oxidation reaction or oxygen reduction reaction (ORR), occur in CLs. The structure of CLs includes a carbon matrix with a Pt catalyst (Pt/C) and proton-conducting ionomers. Importantly, the proton transfer performance of a CL is affected by its ionomer thin film on Pt/C because protons can directly reach the Pt surface through the hydrated ionomer thin film. Therefore, the composition and morphology of the ionomers strongly influence the performance of a PEMFC.
Garsany et al. 13 and Siracusano et al. 14 experimentally investigated PFSA ionomersspecifically, Aquivion, which has a short side chain, and Nafion, which has a long side chain-to improve PEMFC performance. They concluded that Aquivion exhibits better cell performance than Nafion in PEMFCs because the Aquivion ionomer in the cathode CLs has a lower proton transport resistance, lower charge transfer resistance for the ORR, and lower mass transport resistance than the Nafion ionomer. Baschetti et al. 15 investigated gas permeation in Nafion and Aquivion ionomers at various temperatures and relative humidities.
Humidity and temperature have especially strong effects on gas permeability, and Nafion 117 ionomer was found to exhibit greater O2 gas permeability than Aquivion at 50 ℃.
Several groups have investigated the relationship between the diffusion coefficients of water and hydronium ions and PFSA morphologies in systems with various water contents and at different temperatures using molecular dynamics (MD) simulations. [16][17][18][19][20][21] The diffusion coefficients of water and hydronium ions were found to increase with increasing PFSA water content and increasing temperature. In addition, the sulfur-sulfur interatomic distance in PFSA increased with increasing PFSA water content. MD simulations [22][23][24] have also been performed to investigate O2 permeation in Nafion ionomers in CLs. Kurihara et al. 22,23 investigated the permeation of O2 gas into a Nafion ionomer on a Pt surface using MD simulations because such simulations are useful for understanding the nanoscale structures in the CLs of PEMFCs. They concluded that the diffusion coefficient of O2 molecules increased and the solubility of O2 molecules decreased with increasing water content in the Nafion ionomer. Jinnouchi et al. 24 also used MD simulations to investigate O2 permeation through a Nafion thin film on a Pt surface, where the water content of the Nafion film was varied. Their results indicated that O2 permeation in Nafion increased with increasing water content and that understanding the behavior of O2 in PFSA ionomers on a Pt surface is critical to understanding its permeation properties. Therefore, the aforementioned experimental results indicate that the length of the side chain in PFSA ionomers can affect both the performance of PEMFCs and the O2 permeation behavior. Therefore, studies comparing of the O2 permeation properties of Nafion and Aquivion are needed to elucidate the effect of side-chain length in PFSA ionomers in PEMFCs.
In the present study, computational simulations using the full atomistic MD simulation technique are carried out to obtain detailed molecular information for calculating the transport properties of hydrated PFSA ionomers with various water contents on a Pt surface.
In addition, the O2 permeation properties of hydrated PFSA with different side-chain lengths were measured at the interfacial region on the Pt surface. Therefore, two types of PFSA ionomers-Nafion (longer side chain) and Aquivion (shorter side chain)-were prepared for measurement of the O2 permeability at various water contents, enabling the relationship between the hydrated PFSA structure and the O2 permeation properties to be elucidated. In addition, the distribution of O2 and water in PFSA ionomers on a Pt surface were also analyzed using density profiles and radial distribution functions (RDFs) with various water contents at the operating temperature of a PEMFC (353.15 K). We expect that the results of this study will provide detailed information about O2 permeability of water-containing PFSA ionomers on a Pt surface and can provide guidance for the design of PFSA ionomers for use in PEMFCs. Figure 1 shows the chemical structures of the Nafion and Aquivion ionomers. Each ionomer was composed such that each polymer had 10 repeat units with 10 sulfonic acid groups per polymer chain. The molecular weight of the Nafion and Aquivion polymers was 9969.83 g/mol and 8309.63 g/mol per polymer chain; equivalent weights (EWs) of ~1000 g/mol and ~830 g/mol were applied, respectively. Water, O2 molecules, and hydronium ions were prepared for constructing hydrated PFSA ionomers. The components of each PEMFC system are summarized in Table 1.

Force-field and MD parameters
To describe inter-and intramolecular interactions in the Nafion and Aquivion in PEMFC systems, we applied a modified DREIDING force field 25 in our simulations. The DREIDING force field has been widely used to describe PEMFCs systems. [26][27][28][29] The force fields of water molecules and Pt atoms were applied using F3C force field 30 and the embedded-atom method (EAM) force field, respectively. 31 The total potential energy Etotal in PEMFC systems can be calculated using to Eq (1): where vdW , Q , bond , angle , torsion , inversion , and EAM are the van der Waals, electrostatic, bond-stretching, angle-bending, torsion, inversion, and the EAM energies, respectively. For calculating entire MD simulations for PEMFC systems, the large-scale atomic/molecular massively parallel simulator (LAMMPS) code 32,33 from Plimpton at Sandia was used. All MD simulations were carried out using the velocity Ve rlet algorithm 34 to integrate equations of atomic motion, with a time steps of 1 fs. The electrostatic interactions in our systems were calculated using the particle-particle particle-mesh method. 35 The charges of particles in Nafion and Aquivion were calculated via density functional theory (DFT) calculations using the Mulliken charge analysis method 36 in the Materials Studio software. 37 All DFT calculations for charge analyses were carried out using the double numerical basis set with polarization (DNP) function and the generalized gradient approximation with the Perdew-Burke-Ernzerhof functional. 38

Force-field parameters between PEMFC components and the Pt surface
We used the nonbonded interaction energies reported by Brunello et al. 39 to describe the interactions of Pt atoms with Nafion, Aquivion, water, and hydronium ions. In addition, for the interaction energies between O2 and a Pt slab, we calculated van der Waals parameters via DFT calculations to describe detailed intermolecular interactions using a Pt (111) slab with three atomic layers with periodic boundary conditions (PBCs) of 8.324 × 8.324 × 25.000 Å 3 , as shown in Figure 2. The DFT calculation details were the same as those used in the charge analysis (section 2.2.1), and a semi-empirical dispersion correction (DFT-D) with the Tkatchenko-Scheffler scheme was additionally applied. 40 Band-structure calculations with kpoints were performed with a 4 × 4 × 1 Monkhorst-Pack k-point mesh. 41

MD simulations
After the initial hydrated PFSA with Pt (111)

van der Waals parameters for O2 and Pt
For a better description of the O2 permeation process inside a hydrated Nafion ionomer thin film on a Pt (111) surface, the atomic interaction curve between O2 and the Pt surface was reproduced by DFT under the framework of the DREIDING force field. Figure 2(a) shows O2 adsorbed onto the Pt surface, which was built for calculation of the adsorption energy as a function of the z-distance. The calculated adsorption energy as a function of distance was fitted to the Lennard-Jones potential in Figure 2(b), which well reproduced the results of DFT calculations. The Lennard-Jones potential function is shown in Eq (2): where indicates the potential energy with changing distance and is the depth of the potential well at distance m . The values of and m for the oxygen atoms in O2 molecules on a Pt surface are 4.070 kcal/mol and 2.338 Å, respectively. The fitted interaction well describes detailed interactions that the DREIDING force field cannot describe. Thus, the fitted interaction between O2 and Pt surfaces was used in the MD simulation to analyze the process of O2 permeation into a Nafion ionomer coated onto a Pt surface.

Equilibrated structure
Equilibrated structures in Figure 3 To quantitatively analyze the permeation of O2 molecules, we investigated the density profile of hydrated Nafion, water molecules with hydronium ions, and O2 molecules, as shown in  24 , who reported that an energy barrier at the Nafion-gas interface dominates the solubility of O2 in hydrated Nafion. Inside hydrated Nafion, dissolved O2 molecules exhibit the highest density and water molecules with hydronium ions exhibit the lowest density. This trend becomes more discernible as the hydration level increases. These results suggest that O2 molecules are not preferentially positioned inside hydrophilic domains but rather at the interfacial regions between hydrophobic and hydrophilic regions.
We also investigated the density profile of water molecules, hydronium ions, and O2 molecules in hydrated Aquivion; the results are shown in Figure 5(a)-(d). Like Nafion, hydrated Aquivion and water molecules with hydronium ions show the highest density at the Aquivion-Pt interface because of their strong attractive interaction. The hydrated Aquivion is thinner than the hydrated Nafion because of Aquivion's shorter side chains and lower EW.
The density of O2 molecules also abruptly decreases the maximum value at the distance indicated by the purple line, which represents the distance at which O2 solvation begins.
Inside hydrated Aquivion, the dissolved O2 molecules exhibit the highest density and water molecules with hydronium ions exhibit the lowest density.

O2 solubility and permeation
To quantify the solvation of O2 molecules by hydration level, we calculated the solubility on molecules also becomes limited. Therefore, the ionomers exhibit low O2 solubility at high hydration levels (λ). At the same λ, the O2 solubility is higher in the Nafion ionomer than in the Aquivion ionomer, which means that the solvation of O2 molecules in the Aquivion ionomer is restricted compared with that in the Nafion ionomer.
Using the solubility values, we derived the permeability coefficient of O2 molecules. Gases permeate through ionomers via a solution-diffusion mechanism, where the dissolved gas molecules diffuse into the ionomers. 42 Thus, the permeability coefficient P is described by the equation where D is the diffusion coefficient and S is solubility. The diffusion coefficient in our system was obtained from the self-diffusion coefficient of O2 molecules in the bulk structures of Nafion and Aquivion. The calculated permeability coefficients for O2 molecules in Nafion and Aquivion ionomer are shown in Figure 6(b); these values are consistent with those reported by Baschetti et al. 15 . With increasing hydration level λ, the permeability of O2 in both Nafion and Aquivion ionomers increases until λ = 9.77. At λ > 9.77, the permeability increases slightly because, despite the diminished solubility, the self-diffusion coefficient of O2 in a bulk ionomer membrane increases with increasing hydration level; thus, permeability increases with increasing hydration level. In our previous work, 20 we reported that O2 molecules exhibit greater diffusion in Aquivion ionomers than in Nafion ionomers because of the Aquivion ionomers' better-developed water channels. However, at the same hydration level λ, both the permeability and solubility of O2 are higher in Nafion ionomer than in Aquivion ionomer. This result means that solubility is more critical to the permeability, which is dominated by the availability of solvation sites for dissolved O2 molecules in the ionomer.

RDF analysis
The interface region between hydrophilic and hydrophobic domains in a hydrated PFSA ionomer, where O2 molecules preferentially dissolve, is most likely to be the side-chain part above the sulfonic acid groups. That is, O2 solvation mainly occurs at the side chains of the ionomers. Thus, the difference in solubility between Nafion and Aquivion is reasonably deduced to arise from their different side-chain structures. In this regard, we analyzed the structure between O2 and the main component of the Nafion and Aquivion side-chain structures to understand the difference in O2 solubility between them. As shown in Figure   7(a), we analyzed correlations between Carbon(center)-Oxygen(O2) and Oxygen(side chain)-Oxygen(O2) using RDFs. The RDF of each pair is described by the following equation: where is the number of B particles located at a distance r in a shell of thickness from particle A, NB is the number of B particles in the system, and V is the total volume of the system; NB/V can be represented by the number density, ρ. The ρg(r) of each pair of Nafion and Aquivion ionomers is presented in Figure 7 ionomer than in the Aquivion ionomer. This result means that O2 has a more favorable correlation with C(center) and O(side chain) in the Nafion ionomer than with those in the Aquivion ionomer. The first coordination number (CN) at the distance of the first peak was calculated ( Table 2). As shown in Figure 7(d) and (e), the CN of C(center)-O(O2) and O(side chain)-O(O2) pairs also decreases as the hydration level increases with increasing ρg(r). At the same hydration level, the Nafion ionomer shows a higher CN of each pair than the Aquivion ionomer. This result suggests that more O2 molecules are coordinated to the side chain of the Nafion ionomer than to that of the Aquivion ionomer, especially to the side chains' oxygen atoms, which results in greater solubility of O2 in the Nafion ionomer. In addition, we note that that Aquivion shows a similar CN as Nafion at λ = 2.92. As described in the previous section, we also observed that the difference in solubility and permeability is more discernible at a hydration level greater than λ = 2.92. At a low hydration level, the site for O2 solvation is uncertain because of a lack of phase segregation. However, as the hydration level increases, the solvation sites of O2 molecules become limited to the side-chain region of the ionomer. Consequently, Nafion and Aquivion exhibit an observable difference in solubility at higher hydration levels.

Conclusion
We prepared two types of hydrated PFSA ionomers on a Pt (111)